Optimal network topologies for information transmission in active networks

TL;DR

This paper develops a theoretical framework to identify optimal network topologies for information transmission in active networks, such as neural systems, focusing on maximizing information flow, communication channels, and robustness.

Contribution

It introduces a general method to determine optimal network topologies via Laplacian eigenvalues, independent of specific element dynamics.

Findings

Optimal topologies maximize information transmission and robustness.

Method applies to neural networks with chaotic neuron models.

Eigenvalue conditions guide topology design for enhanced communication.

Abstract

This work clarifies the relation between network circuit (topology) and behavior (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how to determine a network topology that is optimal for information transmission. By optimal, we mean that the network is able to transmit a large amount of information, it possesses a large number of communication channels, and it is robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.